Time Travel & Causality in General Relativity

[PeterDonis]

would it be a very weird experience if this occurred?

I would expect so, yes.

Would our memories mess up or something?

I've already addressed this in previous posts. At any point on your worldline, your state is what it is, and it can contain information about the state at other points on your worldline. Whether this fits our intuitive notion of "memory" is not a question of physics but of terminology.